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   "file_extension": ".py",
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 "cells": [
  {
   "source": [
    "# Entanglement of Haar Random State"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mindquantum import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qr_haar(N):\n",
    "    \"\"\"\n",
    "    PennyLane\n",
    "    Generate a Haar-random matrix using the QR decomposition.\n",
    "    \"\"\"\n",
    "    # Step 1\n",
    "    A, B = np.random.normal(size=(N, N)), np.random.normal(size=(N, N))\n",
    "    Z = A + 1j * B\n",
    "\n",
    "    # Step 2\n",
    "    Q, R = np.linalg.qr(Z)\n",
    "\n",
    "    # Step 3\n",
    "    Lambda = np.diag([R[i, i] / np.abs(R[i, i]) for i in range(N)])\n",
    "\n",
    "    # Step 4\n",
    "    return np.dot(Q, Lambda)"
   ]
  },
  {
   "source": [
    "from src.train_nisq import get_rs, s2"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 6,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "n_qubits = 2\n",
    "attempt = 100\n",
    "yyy = np.zeros(attempt)\n",
    "xxx = np.arange(attempt)\n",
    "for n_qubits in [2,3,4,5,6,7]:\n",
    "    for i in range(attempt):\n",
    "        qs = qr_haar(2**n_qubits)[:,0]\n",
    "        rho = np.outer(qs, qs.conjugate())\n",
    "        yyy[i] = s2(get_rs(rho,[0]))\n",
    "    plt.subplot(2,3,n_qubits-1)\n",
    "    plt.title(f'n_qubits={n_qubits}')\n",
    "    plt.ylim((0,1))\n",
    "    plt.scatter(xxx,yyy, marker = 'x')\n",
    "plt.suptitle('Concentration of 2nd Renyi entropy in first qubit', fontsize = 15)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 6 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "n_qubits = 2\n",
    "attempt = 100\n",
    "yyy = np.zeros(attempt)\n",
    "xxx = np.arange(attempt)\n",
    "for n_qubits in [2,3,4,5,6,7]:\n",
    "    for i in range(attempt):\n",
    "        qs = qr_haar(2**n_qubits)[:,0]\n",
    "        rho = np.outer(qs, qs.conjugate())\n",
    "        yyy[i] = s2(get_rs(rho,[0,1]))\n",
    "    plt.subplot(2,3,n_qubits-1)\n",
    "    plt.title(f'n_qubits={n_qubits}')\n",
    "    plt.ylim((0,2))\n",
    "    plt.scatter(xxx,yyy, marker = 'x')\n",
    "plt.suptitle('Concentration of 2nd Renyi entropy in first 2 qubits', fontsize = 15)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ]
}